Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids

TL;DR

This paper investigates how Anderson acceleration improves the convergence of a fixed-point iterative solver for the Oldroyd-B model, a key system in simulating viscoelastic fluid flows, especially at high Weissenberg numbers.

Contribution

The study establishes conditions for the fixed-point solver's contractiveness and demonstrates that Anderson acceleration enhances its linear convergence rate for the Oldroyd-B system.

Findings

AA improves convergence speed at high Weissenberg numbers

The fixed-point solver is contractive under certain smoothness conditions

Benchmark tests confirm the effectiveness of AA in viscoelastic fluid simulations

Abstract

We study an iterative nonlinear solver for the Oldroyd-B system describing incompressible viscoelastic fluid flow. We establish a range of attributes of the fixed-point-based solver, together with the conditions under which it becomes contractive and examining the smoothness properties of its corresponding fixed-point function. Under these properties, we demonstrate that the solver meets the necessary conditions for recent Anderson acceleration (AA) framework, thereby showing that AA enhances the solver's linear convergence rate. Results from two benchmark tests illustrate how AA improves the solver's ability to converge as the Weissenberg number is increased.